He has previously expressed hopes of playing for the 23-time Ghanaian champions before hanging up his boots.
“Kotoko have said they like him because he once stated that he’ll one day play for Kotoko, but for now, no club has approached him with any offer,” Anim Addo told Graphic Sports.
“Gyan has had offers from Europe and Asia but if Kotoko can meet our terms, then why not?”
Kotoko defender Habib Mohammed will welcome a move for the 34-year-old veteran who is Africa's highest scorer at the Fifa World Cup, with six goals.
“I will be very happy if I see Asamoah Gyan join Kotoko because he will help the team in terms of experience," said the centre-back, reports FootballGhana.
“The players will also be proud of playing with the [former] Black Stars captain."
In 2013, Gyan, who played for Liberty Professionals during his time in the domestic league, told Angel FM: "I will definitely return one day to the Ghana Premier League where I will play for no other club than Asante Kotoko.
''I have and always been a big fan of Kotoko and always wish the club win games and trophies."
The striker reiterated his desire in 2018, saying, “I have said it over and over again. I am definitely going to play for Kotoko.
“It’s official and confirmed - people know and I always say it. I am going to play for Kumasi Asante Kotoko before I retire," he was reported by Ghana Sports Online as saying.